Details

analyze1.1s (18%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

Compiler

Compiled 15 to 13 computations (13.3% saved)

sample40.0ms (0.6%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
4.0ms	79×	body	128	nan
2.0ms	32×	body	128	invalid

Compiler

Compiled 29 to 30 computations (-3.4% saved)

simplify172.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	175	21
1	175	21

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 24.2b

Counts

2 → 1

Compiler

Compiled 28 to 24 computations (14.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 z z) (.f64 t a))
5.6b	(.f64 (.f64 x y) z)
9.6b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
22.7b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_10559` `add-cbrt-cube_binary64_10557`
11×	`add-sqr-sqrt_binary64_10545`
10×	`pow1_binary64_10582` `*-un-lft-identity_binary64_10524` `add-cube-cbrt_binary64_10556`
9×	`sqrt-prod_binary64_10539`
6×	`prod-exp_binary64_10570` `cbrt-unprod_binary64_10554` `times-frac_binary64_10530` `add-log-exp_binary64_10560` `associate-/r*_binary64_10470`
4×	`sqrt-div_binary64_10540`
3×	`flip--_binary64_10499` `flip3--_binary64_10528` `pow-prod-down_binary64_10592` `div-exp_binary64_10572` `cbrt-undiv_binary64_10555` `associate-r_binary64_10466`
2×	`associate-/r/_binary64_10472`
1×	`sub-neg_binary64_10517` `rem-sqrt-square_binary64_10537` `-commutative_binary64_10457` `sqrt-pow1_binary64_10541` `associate-/l_binary64_10471` `frac-2neg_binary64_10535` `pow1/2_binary64_10601` `associate-l_binary64_10467` `clear-num_binary64_10523` `div-inv_binary64_10521` `diff-log_binary64_10613`

Counts

4 → 75

Calls

4 calls:

11.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
5.0ms	(.f64 (.f64 x y) z)
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series473.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

254.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
108.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
59.0ms	(-.f64 (.f64 z z) (.f64 t a))
52.0ms	(.f64 (.f64 x y) z)

simplify53.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5153	1466

prune95.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	79	8	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	8	88

Merged error: 4.0b

Counts

88 → 8

Compiler

Compiled 1751 to 351 computations (80% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
1.2b	(-.f64 (.f64 z z) (.f64 t a))
3.9b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
22.7b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite40.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64_10530`
34×	`add-sqr-sqrt_binary64_10545`
33×	`*-un-lft-identity_binary64_10524` `add-cube-cbrt_binary64_10556`
24×	`sqrt-prod_binary64_10539` `associate-r_binary64_10466`
18×	`add-exp-log_binary64_10559` `add-cbrt-cube_binary64_10557`
10×	`pow1_binary64_10582`
6×	`prod-exp_binary64_10570` `cbrt-unprod_binary64_10554` `add-log-exp_binary64_10560` `sqrt-div_binary64_10540` `associate-/r*_binary64_10470`
4×	`flip--_binary64_10499` `flip3--_binary64_10528` `associate-/r/_binary64_10472`
3×	`pow-prod-down_binary64_10592` `associate-/l*_binary64_10471` `div-exp_binary64_10572` `cbrt-undiv_binary64_10555`
2×	`div-inv_binary64_10521`
1×	`sub-neg_binary64_10517` `rem-sqrt-square_binary64_10537` `-commutative_binary64_10457` `sqrt-pow1_binary64_10541` `frac-2neg_binary64_10535` `associate-r/_binary64_10468` `pow1/2_binary64_10601` `associate-l_binary64_10467` `clear-num_binary64_10523` `diff-log_binary64_10613`

Counts

4 → 111

Calls

4 calls:

14.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
7.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series495.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

248.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
107.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
85.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
54.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify74.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5237	2515

prune99.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	122	9	131

Merged error: 3.8b

Counts

131 → 9

Compiler

Compiled 2767 to 483 computations (82.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 z z) (.f64 t a))
3.9b	(.f64 (.f64 x y) (/.f64 (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
22.7b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
22.7b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite179.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

546×	`sqrt-prod_binary64_10539`
540×	`times-frac_binary64_10530`
303×	`associate-r_binary64_10466`
279×	`add-sqr-sqrt_binary64_10545`
277×	`*-un-lft-identity_binary64_10524` `add-cube-cbrt_binary64_10556`
44×	`sqrt-div_binary64_10540`
25×	`add-exp-log_binary64_10559` `add-cbrt-cube_binary64_10557`
20×	`associate-/r/_binary64_10472`
13×	`flip--_binary64_10499` `flip3--_binary64_10528`
11×	`pow1_binary64_10582`
10×	`div-inv_binary64_10521`
9×	`prod-exp_binary64_10570` `cbrt-unprod_binary64_10554`
6×	`div-exp_binary64_10572` `add-log-exp_binary64_10560` `cbrt-undiv_binary64_10555`
3×	`pow-prod-down_binary64_10592`
2×	`rem-sqrt-square_binary64_10537` `sqrt-pow1_binary64_10541` `pow1/2_binary64_10601`
1×	`sub-neg_binary64_10517` `-commutative_binary64_10457` `associate-r/_binary64_10468` `associate-l_binary64_10467` `diff-log_binary64_10613`

Counts

4 → 368

Calls

4 calls:

78.0ms	(.f64 (.f64 x y) (/.f64 (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series510.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

257.0ms	(.f64 (.f64 x y) (/.f64 (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
105.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
100.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
48.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify140.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

380 → 380

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5012	11813

prune383.0ms (6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	380	0	380
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	380	9	389

Merged error: 3.8b

Counts

389 → 9

Compiler

Compiled 15988 to 980 computations (93.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 z z) (.f64 t a))
2.0b	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
2.9b	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
22.7b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_10545`
25×	`associate-r_binary64_10466`
20×	`times-frac_binary64_10530` `*-un-lft-identity_binary64_10524` `add-cube-cbrt_binary64_10556`
18×	`add-exp-log_binary64_10559` `add-cbrt-cube_binary64_10557`
13×	`sqrt-prod_binary64_10539`
12×	`pow1_binary64_10582`
7×	`prod-exp_binary64_10570` `cbrt-unprod_binary64_10554`
6×	`associate-l_binary64_10467` `add-log-exp_binary64_10560`
4×	`pow-prod-down_binary64_10592` `sqrt-div_binary64_10540`
3×	`flip--_binary64_10499` `flip3--_binary64_10528` `associate-*r/_binary64_10468` `unswap-sqr_binary64_10492`
2×	`*-commutative_binary64_10457` `div-exp_binary64_10572` `associate-/r/_binary64_10472` `cbrt-undiv_binary64_10555`
1×	`sub-neg_binary64_10517` `rem-sqrt-square_binary64_10537` `sqrt-pow1_binary64_10541` `pow1/2_binary64_10601` `div-inv_binary64_10521` `diff-log_binary64_10613`

Counts

4 → 91

Calls

4 calls:

14.0ms	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
11.0ms	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

series526.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

240.0ms	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
143.0ms	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
93.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
50.0ms	(-.f64 (.f64 z z) (.f64 t a))

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5151	1891

prune74.0ms (1.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	103	9	112

Merged error: 3.8b

Counts

112 → 9

Compiler

Compiled 2092 to 386 computations (81.5% saved)

regimes222.0ms (3.5%)

Compiler: Compiled 1002 to 816 computations (18.6% saved)

bsearch54.0ms (0.9%)

Steps

Iters	Range		Point
8	7.577880983078945e+105	4.07845131805606e+108	2.519421385402226e+106
10	-1.8636698370338714e+159	-4.0744833840128644e+147	-6.785471256713384e+153

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	43
1	71	43

end0.0ms (0%)

sample1.4s (21.8%)

Algorithm

1×

intervals

Results

438.0ms	8000×	body	128	valid
107.0ms	2252×	body	128	nan
47.0ms	858×	body	128	invalid

Compiler

Compiled 213 to 163 computations (23.5% saved)

Details

analyze1.1s (18%)

sample40.0ms (0.6%)

simplify172.0ms (2.7%)

prune3.0ms (0%)

localize15.0ms (0.2%)

rewrite30.0ms (0.5%)

series473.0ms (7.5%)

simplify53.0ms (0.8%)

prune95.0ms (1.5%)

localize10.0ms (0.2%)

rewrite40.0ms (0.6%)

series495.0ms (7.8%)

simplify74.0ms (1.2%)

prune99.0ms (1.6%)

localize13.0ms (0.2%)

rewrite179.0ms (2.8%)

series510.0ms (8.1%)

simplify140.0ms (2.2%)

prune383.0ms (6%)

localize13.0ms (0.2%)

rewrite43.0ms (0.7%)

series526.0ms (8.3%)

simplify58.0ms (0.9%)

prune74.0ms (1.2%)

regimes222.0ms (3.5%)

bsearch54.0ms (0.9%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.4s (21.8%)

Profiling